Question

The value of $x$ for which the value of the function $f\left(x\right)=-\frac{11}{3}{x}^2+17x-\frac{43}{13}$ is maximum is

• A. $x=-\frac{102}{11}$
• B. $x=-\frac{51}{22}$
• C. $x=\frac{51}{22}$
• D. $x=\frac{102}{11}$

Answer 1

Answer: (C)

$x=\frac{51}{22}$

Given, $f\left(x\right)=\frac{-11}{3}{x}^2+17x-\frac{43}{13}$

Since we need where the maximum value is attained, we differentiate the function w.r.t. $x$.

And get $\frac{d\left(f\right(x\left)\right)}{dx}=\frac{-11\times 2}{3}x+17$

Equating the above equation to zero gives $x=\frac{17\times 3}{11\times 2}=\frac{51}{22}$